exercise_07

Exercise 07

Geometry Processing Research in Python

Randomness

For many applications in geometry processing we want to incorporate an element of randomness. Maybe we want a random initialization for an algorithm, or we just want to select places to do something without any regularity. In this exercise you will learn how randomness works in Gpytoolbox, and how to maintain good scientific practice when using randomness in your research.

Sampling random points - Here's what not to do!

If you want to sample random points on a surface uniformly, Gpytoolbox has a simple function for that: random_points_on_mesh. It takes in the surface, as well as the number of points you are sampling.

import gpytoolbox as gpy, numpy as np, polyscope as ps
V,F = gpy.read_mesh("data/penguin.obj")
P = gpy.random_points_on_mesh(V, F, 300)
ps.init()
ps_penguin = ps.register_surface_mesh("penguin", V, F,
    material='wax', smooth_shade=True)
ps_pts = ps.register_point_cloud("random points", P)
ps.show()

This displays:

This seems fine. But what if we run the same script again?

Those are different points than last time! On one hand, of course, this makes sense: You asked for random points, so why would you get the same set of random points both times? But if you are a scientist, you should aim for your work to be reproducible.

Reproducible randomness

In order to create reproducible scripts, we can seed the random number engine with a constant seed, making sure that it always reproduces the same results when a script is run again.

Gpytoolbox (mostly) uses the NumPy randomness paradigm: A random generator, which gets passed to every function that needs random numbers, controls random number generation throughout the entire script. You can initialize it with:

import numpy as np
rng = np.random.default_rng()
print(f"A random number: {rng.random()}")
print(f"Another random number: {rng.random()}")

This prints:

A random number: 0.4975738858606218
Another random number: 0.3865480452803277

Of course it only prints this on my computer, not on yours. If you initialize a NumPy default_rng without any arguments, it gets randomness from a reliably random source, usually a piece of hardware in your computer. Case in point, if I run this script a second time, I get:

A random number: 0.036213920801204
Another random number: 0.9806510984456254

This is great for cryptographic safety, but bad for reproducibility. We can create a reproducible NumPy rng by seeding it with a fixed integer:

import numpy as np
seed = 8745932
rng = np.random.default_rng(seed)
print(f"A random number: {rng.random()}")
print(f"Another random number: {rng.random()}")

This prints:

A random number: 0.37597233604132463
Another random number: 0.1206232325698362

If I run it again:

A random number: 0.37597233604132463
Another random number: 0.1206232325698362

Reproducible randomness in Gpytoolbox

Gpytoolbox functions with randomness capability accept a NumPy rng object to allow you to write reproducible programs. The random_points_on_mesh function works as follows:

import gpytoolbox as gpy, numpy as np, polyscope as ps
seed = 8745932
rng = np.random.default_rng(seed)
V,F = gpy.read_mesh("data/penguin.obj")
P = gpy.random_points_on_mesh(V, F, 300, rng=rng)
ps.init()
ps_penguin = ps.register_surface_mesh("penguin", V, F,
    material='wax', smooth_shade=True)
ps_pts = ps.register_point_cloud("random points", P)
ps.show()

This displays:

If I run it a second time, I get exactly the same result

NOTE: Some Gpytoolbox functions will take seeds directly, and not rng objects. For these, you ran generate a seed from your rng object with rng.integers(np.iinfo(np.int32).max).

That's it!

The next exercise, exercise_08, will teach you how to build and use finite element matrices.

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Oded Stein 2024. Geometry Processing Research in Python